Clustering and classification (Exercise 4)
library(MASS);library(tidyverse);library(corrplot)## -- Attaching packages ------------------------------------------------------------------------------------- tidyverse 1.2.1 --## v ggplot2 3.2.1 v purrr 0.3.3
## v tibble 2.1.3 v dplyr 0.8.3
## v tidyr 1.0.0 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.4.0## -- Conflicts ---------------------------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x dplyr::select() masks MASS::select()## corrplot 0.84 loadeddata("Boston")The data has 506 observations and 14 variables. Data is about housing values in suburbs of Boston.
Explort dataset
str(Boston)## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...summary(Boston)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08204 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio black
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## lstat medv
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00pairs(Boston)
Correlate all variables
cor_matrix<-cor(Boston)
cor_matrix%>%round(2)## crim zn indus chas nox rm age dis rad tax
## crim 1.00 -0.20 0.41 -0.06 0.42 -0.22 0.35 -0.38 0.63 0.58
## zn -0.20 1.00 -0.53 -0.04 -0.52 0.31 -0.57 0.66 -0.31 -0.31
## indus 0.41 -0.53 1.00 0.06 0.76 -0.39 0.64 -0.71 0.60 0.72
## chas -0.06 -0.04 0.06 1.00 0.09 0.09 0.09 -0.10 -0.01 -0.04
## nox 0.42 -0.52 0.76 0.09 1.00 -0.30 0.73 -0.77 0.61 0.67
## rm -0.22 0.31 -0.39 0.09 -0.30 1.00 -0.24 0.21 -0.21 -0.29
## age 0.35 -0.57 0.64 0.09 0.73 -0.24 1.00 -0.75 0.46 0.51
## dis -0.38 0.66 -0.71 -0.10 -0.77 0.21 -0.75 1.00 -0.49 -0.53
## rad 0.63 -0.31 0.60 -0.01 0.61 -0.21 0.46 -0.49 1.00 0.91
## tax 0.58 -0.31 0.72 -0.04 0.67 -0.29 0.51 -0.53 0.91 1.00
## ptratio 0.29 -0.39 0.38 -0.12 0.19 -0.36 0.26 -0.23 0.46 0.46
## black -0.39 0.18 -0.36 0.05 -0.38 0.13 -0.27 0.29 -0.44 -0.44
## lstat 0.46 -0.41 0.60 -0.05 0.59 -0.61 0.60 -0.50 0.49 0.54
## medv -0.39 0.36 -0.48 0.18 -0.43 0.70 -0.38 0.25 -0.38 -0.47
## ptratio black lstat medv
## crim 0.29 -0.39 0.46 -0.39
## zn -0.39 0.18 -0.41 0.36
## indus 0.38 -0.36 0.60 -0.48
## chas -0.12 0.05 -0.05 0.18
## nox 0.19 -0.38 0.59 -0.43
## rm -0.36 0.13 -0.61 0.70
## age 0.26 -0.27 0.60 -0.38
## dis -0.23 0.29 -0.50 0.25
## rad 0.46 -0.44 0.49 -0.38
## tax 0.46 -0.44 0.54 -0.47
## ptratio 1.00 -0.18 0.37 -0.51
## black -0.18 1.00 -0.37 0.33
## lstat 0.37 -0.37 1.00 -0.74
## medv -0.51 0.33 -0.74 1.00corrplot(cor_matrix, method="circle", type="upper", cl.pos="b", tl.pos="d", tl.cex=0.6)
There is strongly positive correlation bewtween “rad” and “tax” and stongly negative correlation between “age” and “dis” and between “lstat” and “medv”.
Standardized data
boston_scaled<-scale(Boston)
summary(boston_scaled)## crim zn indus
## Min. :-0.419367 Min. :-0.48724 Min. :-1.5563
## 1st Qu.:-0.410563 1st Qu.:-0.48724 1st Qu.:-0.8668
## Median :-0.390280 Median :-0.48724 Median :-0.2109
## Mean : 0.000000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.007389 3rd Qu.: 0.04872 3rd Qu.: 1.0150
## Max. : 9.924110 Max. : 3.80047 Max. : 2.4202
## chas nox rm age
## Min. :-0.2723 Min. :-1.4644 Min. :-3.8764 Min. :-2.3331
## 1st Qu.:-0.2723 1st Qu.:-0.9121 1st Qu.:-0.5681 1st Qu.:-0.8366
## Median :-0.2723 Median :-0.1441 Median :-0.1084 Median : 0.3171
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.:-0.2723 3rd Qu.: 0.5981 3rd Qu.: 0.4823 3rd Qu.: 0.9059
## Max. : 3.6648 Max. : 2.7296 Max. : 3.5515 Max. : 1.1164
## dis rad tax ptratio
## Min. :-1.2658 Min. :-0.9819 Min. :-1.3127 Min. :-2.7047
## 1st Qu.:-0.8049 1st Qu.:-0.6373 1st Qu.:-0.7668 1st Qu.:-0.4876
## Median :-0.2790 Median :-0.5225 Median :-0.4642 Median : 0.2746
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6617 3rd Qu.: 1.6596 3rd Qu.: 1.5294 3rd Qu.: 0.8058
## Max. : 3.9566 Max. : 1.6596 Max. : 1.7964 Max. : 1.6372
## black lstat medv
## Min. :-3.9033 Min. :-1.5296 Min. :-1.9063
## 1st Qu.: 0.2049 1st Qu.:-0.7986 1st Qu.:-0.5989
## Median : 0.3808 Median :-0.1811 Median :-0.1449
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.4332 3rd Qu.: 0.6024 3rd Qu.: 0.2683
## Max. : 0.4406 Max. : 3.5453 Max. : 2.9865Covert matrix data to dafaframe
class(boston_scaled)## [1] "matrix"boston_scaled<-as.data.frame(boston_scaled)Create a catergorical variable with the variable “Crime”
summary("crim")## Length Class Mode
## 1 character characterbins<-quantile(boston_scaled$crim)
bins## 0% 25% 50% 75% 100%
## -0.419366929 -0.410563278 -0.390280295 0.007389247 9.924109610crime<-cut(boston_scaled$crim, breaks=bins, include.lowest=TRUE, label=c("low","med_low","med_high", "high"))
crime## [1] low low low low low low med_low
## [8] med_low med_low med_low med_low med_low med_low med_high
## [15] med_high med_high med_high med_high med_high med_high med_high
## [22] med_high med_high med_high med_high med_high med_high med_high
## [29] med_high med_high med_high med_high med_high med_high med_high
## [36] low med_low low med_low low low med_low
## [43] med_low med_low med_low med_low med_low med_low med_low
## [50] med_low med_low low low low low low
## [57] low low med_low med_low med_low med_low med_low
## [64] med_low low low low low med_low med_low
## [71] med_low med_low med_low med_low low med_low med_low
## [78] med_low low med_low low low low low
## [85] low low low low low low low
## [92] low low low low med_low med_low med_low
## [99] low low med_low med_low med_low med_low med_low
## [106] med_low med_low med_low med_low med_high med_low med_low
## [113] med_low med_low med_low med_low med_low med_low med_low
## [120] med_low low low med_low med_low med_low med_low
## [127] med_high med_high med_high med_high med_high med_high med_high
## [134] med_high med_high med_high med_high med_high med_low med_high
## [141] med_high med_high med_high high med_high med_high med_high
## [148] med_high med_high med_high med_high med_high med_high med_high
## [155] med_high med_high med_high med_high med_high med_high med_high
## [162] med_high med_high med_high med_high med_high med_high med_high
## [169] med_high med_high med_high med_high med_low med_low med_low
## [176] low low low low low low low
## [183] med_low med_low med_low low low low med_low
## [190] med_low med_low low med_low low low low
## [197] low low low low low low low
## [204] low low med_low med_low med_low med_low med_high
## [211] med_low med_high med_low med_low med_high med_low low
## [218] low med_low med_low med_high med_high med_high med_high
## [225] med_high med_high med_high med_high med_high med_high med_high
## [232] med_high med_high med_high med_high med_high med_high med_high
## [239] med_low med_low med_low med_low med_low med_low med_low
## [246] med_low med_high med_low med_low med_low med_low med_low
## [253] med_low med_high low low low med_high med_high
## [260] med_high med_high med_high med_high med_high med_high med_high
## [267] med_high med_high med_high med_low med_high med_low med_low
## [274] med_low low med_low med_low low low med_low
## [281] low low low low low low low
## [288] low low low low low low med_low
## [295] low med_low low med_low low low low
## [302] low med_low med_low low low low low
## [309] med_high med_high med_high med_high med_high med_high med_high
## [316] med_low med_high med_low med_high med_high med_low med_low
## [323] med_high med_high med_high med_low med_high med_low low
## [330] low low low low low low low
## [337] low low low low low low low
## [344] low low low low low low low
## [351] low low low low low med_low high
## [358] high high high high high high high
## [365] med_high high high high high high high
## [372] high high high high high high high
## [379] high high high high high high high
## [386] high high high high high high high
## [393] high high high high high high high
## [400] high high high high high high high
## [407] high high high high high high high
## [414] high high high high high high high
## [421] high high high high high high high
## [428] high high high high high high high
## [435] high high high high high high high
## [442] high high high high high high high
## [449] high high high high high high high
## [456] high high high high high high high
## [463] high high high med_high high high high
## [470] high high high med_high high high high
## [477] high high high high high high high
## [484] med_high med_high med_high high high med_low med_low
## [491] med_low med_low med_low med_low med_high med_low med_high
## [498] med_high med_low med_low med_low low low low
## [505] med_low low
## Levels: low med_low med_high hightable(crime)## crime
## low med_low med_high high
## 127 126 126 127Remove original “crim” from the dataset and add the new categorial variable
boston_scaled<-dplyr::select(boston_scaled,-crim)
boston_scaled## zn indus chas nox rm
## 1 0.28454827 -1.28663623 -0.2723291 -0.14407485 0.413262920
## 2 -0.48724019 -0.59279438 -0.2723291 -0.73953036 0.194082387
## 3 -0.48724019 -0.59279438 -0.2723291 -0.73953036 1.281445551
## 4 -0.48724019 -1.30558569 -0.2723291 -0.83445805 1.015297761
## 5 -0.48724019 -1.30558569 -0.2723291 -0.83445805 1.227362043
## 6 -0.48724019 -1.30558569 -0.2723291 -0.83445805 0.206891639
## 7 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.388026950
## 8 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.160306916
## 9 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.930285282
## 10 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.399412952
## 11 0.04872402 -0.47618230 -0.2723291 -0.26489191 0.131459378
## 12 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.392296701
## 13 0.04872402 -0.47618230 -0.2723291 -0.26489191 -0.563086727
## 14 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.477691714
## 15 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.268473932
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## 28 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.338213193
## 29 -0.48724019 -0.43682573 -0.2723291 -0.14407485 0.299402903
## 30 -0.48724019 -0.43682573 -0.2723291 -0.14407485 0.554164692
## 31 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.813578764
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## 33 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.476268464
## 34 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.830657767
## 35 -0.48724019 -0.43682573 -0.2723291 -0.14407485 -0.268473932
## 36 -0.48724019 -0.75459363 -0.2723291 -0.48063666 -0.500463717
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## 38 -0.48724019 -0.75459363 -0.2723291 -0.48063666 -0.618593485
## 39 -0.48724019 -0.75459363 -0.2723291 -0.48063666 -0.453496460
## 40 2.72854505 -1.19334657 -0.2723291 -1.09335175 0.441727925
## 41 2.72854505 -1.19334657 -0.2723291 -1.09335175 1.052302267
## 42 -0.48724019 -0.61611679 -0.2723291 -0.92075595 0.690796712
## 43 -0.48724019 -0.61611679 -0.2723291 -0.92075595 -0.164576667
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## 48 -0.48724019 -0.61611679 -0.2723291 -0.92075595 -0.362408446
## 49 -0.48724019 -0.61611679 -0.2723291 -0.92075595 -1.260479332
## 50 -0.48724019 -0.61611679 -0.2723291 -0.92075595 -0.971559538
## 51 0.41317968 -0.80123846 -0.2723291 -0.99842406 -0.457766211
## 52 0.41317968 -0.80123846 -0.2723291 -0.99842406 -0.241432178
## 53 0.41317968 -0.80123846 -0.2723291 -0.99842406 0.322174907
## 54 0.41317968 -0.80123846 -0.2723291 -0.99842406 -0.407952453
## 55 2.72854505 -1.04029322 -0.2723291 -1.24868797 -0.564509977
## 56 3.37170210 -1.44552019 -0.2723291 -1.30909650 1.372533565
## 57 3.15731641 -1.51548743 -0.2723291 -1.24868797 0.139998879
## 58 3.80047346 -1.43094368 -0.2723291 -1.24005818 0.756266222
## 59 0.58468822 -0.87557866 -0.2723291 -0.87760700 -0.198734672
## 60 0.58468822 -0.87557866 -0.2723291 -0.87760700 -0.509003218
## 61 0.58468822 -0.87557866 -0.2723291 -0.87760700 -0.773727758
## 62 0.58468822 -0.87557866 -0.2723291 -0.87760700 -0.453496460
## 63 0.58468822 -0.87557866 -0.2723291 -0.87760700 0.243896145
## 64 0.58468822 -0.87557866 -0.2723291 -0.87760700 0.679410711
## 65 0.26310970 -1.42219777 -0.2723291 -1.19604625 1.166162284
## 66 2.94293073 -1.13212523 -0.2723291 -1.35224545 0.007636609
## 67 2.94293073 -1.13212523 -0.2723291 -1.35224545 -0.708258248
## 68 0.04872402 -0.73855947 -0.2723291 -1.25731776 -0.578742479
## 69 0.04872402 -0.73855947 -0.2723291 -1.25731776 -0.982945540
## 70 0.04872402 -0.73855947 -0.2723291 -1.25731776 -0.568779727
## 71 -0.48724019 -0.04763292 -0.2723291 -1.22279860 0.188389387
## 72 -0.48724019 -0.04763292 -0.2723291 -1.22279860 -0.460612711
## 73 -0.48724019 -0.04763292 -0.2723291 -1.22279860 -0.312594689
## 74 -0.48724019 -0.04763292 -0.2723291 -1.22279860 -0.056409650
## 75 -0.48724019 0.24681257 -0.2723291 -1.01568364 -0.016558644
## 76 -0.48724019 0.24681257 -0.2723291 -1.01568364 0.001943608
## 77 -0.48724019 0.24681257 -0.2723291 -1.01568364 -0.008019143
## 78 -0.48724019 0.24681257 -0.2723291 -1.01568364 -0.205850923
## 79 -0.48724019 0.24681257 -0.2723291 -1.01568364 -0.074911903
## 80 -0.48724019 0.24681257 -0.2723291 -1.01568364 -0.584435480
## 81 0.58468822 -0.91493524 -0.2723291 -1.11061133 0.629596953
## 82 0.58468822 -0.91493524 -0.2723291 -1.11061133 0.475885930
## 83 0.58468822 -0.91493524 -0.2723291 -1.11061133 0.024715612
## 84 0.58468822 -0.91493524 -0.2723291 -1.11061133 -0.167423167
## 85 -0.48724019 -0.96886832 -0.2723291 -0.91212616 0.148538381
## 86 -0.48724019 -0.96886832 -0.2723291 -0.91212616 0.491541682
## 87 -0.48724019 -0.96886832 -0.2723291 -0.91212616 -0.383757200
## 88 -0.48724019 -0.96886832 -0.2723291 -0.91212616 -0.232892677
## 89 -0.48724019 -1.12629463 -0.2723291 -0.56693456 1.028107013
## 90 -0.48724019 -1.12629463 -0.2723291 -0.56693456 1.130581029
## 91 -0.48724019 -1.12629463 -0.2723291 -0.56693456 0.188389387
## 92 -0.48724019 -1.12629463 -0.2723291 -0.56693456 0.171310384
## 93 0.71331963 0.56895343 -0.2723291 -0.78267931 0.223970642
## 94 0.71331963 0.56895343 -0.2723291 -0.78267931 -0.104800158
## 95 0.71331963 0.56895343 -0.2723291 -0.78267931 -0.050716649
## 96 -0.48724019 -1.20209248 -0.2723291 -0.94664532 0.484425431
## 97 -0.48724019 -1.20209248 -0.2723291 -0.94664532 -0.173116168
## 98 -0.48724019 -1.20209248 -0.2723291 -0.94664532 2.539598741
## 99 -0.48724019 -1.20209248 -0.2723291 -0.94664532 2.185209437
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## 339 -0.48724019 -0.86683276 -0.2723291 -0.34256002 -0.321134190
## 340 -0.48724019 -0.86683276 -0.2723291 -0.34256002 -0.426454706
## 341 -0.48724019 -0.86683276 -0.2723291 -0.34256002 -0.450649960
## 342 1.01345959 -1.40179066 -0.2723291 -0.97253469 1.361147563
## 343 -0.48724019 -1.34785757 -0.2723291 -0.31667065 0.363449163
## 344 1.87100232 -1.07236154 -0.2723291 -0.61008351 0.585476196
## 345 1.87100232 -1.07236154 -0.2723291 -0.61008351 0.838814735
## 346 -0.48724019 -0.98344483 -0.2723291 -0.97253469 -0.385180450
## 347 -0.48724019 -0.98344483 -0.2723291 -0.97253469 -0.550277475
## 348 3.15731641 -1.01842846 -0.2723291 -1.08472196 0.329291158
## 349 2.94293073 -1.33036576 -0.2723291 -1.03294322 0.498657933
## 350 1.22784527 -1.44114723 -0.2723291 -1.08472196 0.931325998
## 351 1.22784527 -1.44114723 -0.2723291 -1.08472196 0.292286652
## 352 2.08538800 -1.37701059 -0.2723291 -1.24005818 0.418955921
## 353 2.08538800 -1.37701059 -0.2723291 -1.24005818 -0.570202978
## 354 3.37170210 -1.32890811 -0.2723291 -1.24868797 0.631020203
## 355 2.94293073 -1.34494227 -0.2723291 -1.22279860 -0.884741275
## 356 2.94293073 -1.34494227 -0.2723291 -1.22279860 -0.496193967
## 357 -0.48724019 1.01499462 3.6647712 1.85803641 -0.103376907
## 358 -0.48724019 1.01499462 3.6647712 1.85803641 0.157077882
## 359 -0.48724019 1.01499462 3.6647712 1.85803641 -0.224353176
## 360 -0.48724019 1.01499462 -0.2723291 1.85803641 -0.245701929
## 361 -0.48724019 1.01499462 -0.2723291 1.85803641 0.161347633
## 362 -0.48724019 1.01499462 -0.2723291 1.85803641 -0.047870149
## 363 -0.48724019 1.01499462 -0.2723291 1.85803641 -1.313139590
## 364 -0.48724019 1.01499462 3.6647712 1.85803641 -0.685486245
## 365 -0.48724019 1.01499462 3.6647712 1.40928733 3.551529643
## 366 -0.48724019 1.01499462 -0.2723291 1.40928733 -3.876413226
## 367 -0.48724019 1.01499462 -0.2723291 1.40928733 -1.881016425
## 368 -0.48724019 1.01499462 -0.2723291 0.65849561 -3.446591661
## 369 -0.48724019 1.01499462 -0.2723291 0.65849561 -1.871053674
## 370 -0.48724019 1.01499462 3.6647712 0.65849561 0.566973944
## 371 -0.48724019 1.01499462 3.6647712 0.65849561 1.040916265
## 372 -0.48724019 1.01499462 -0.2723291 0.65849561 -0.097683907
## 373 -0.48724019 1.01499462 3.6647712 0.97779784 -0.583012230
## 374 -0.48724019 1.01499462 -0.2723291 0.97779784 -1.962141687
## 375 -0.48724019 1.01499462 -0.2723291 0.97779784 -3.055197852
## 376 -0.48724019 1.01499462 -0.2723291 1.00368721 1.463621579
## 377 -0.48724019 1.01499462 -0.2723291 1.00368721 0.518583436
## 378 -0.48724019 1.01499462 -0.2723291 1.00368721 0.724954717
## 379 -0.48724019 1.01499462 -0.2723291 1.00368721 0.135729129
## 380 -0.48724019 1.01499462 -0.2723291 1.00368721 -0.087721155
## 381 -0.48724019 1.01499462 -0.2723291 1.00368721 0.972600255
## 382 -0.48724019 1.01499462 -0.2723291 1.00368721 0.370565414
## 383 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.065494052
## 384 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.088266056
## 385 -0.48724019 1.01499462 -0.2723291 1.25395112 -2.727850303
## 386 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.434115858
## 387 -0.48724019 1.01499462 -0.2723291 1.25395112 -2.323647242
## 388 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.828356167
## 389 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.999146193
## 390 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.273288584
## 391 -0.48724019 1.01499462 -0.2723291 1.25395112 -0.813578764
## 392 -0.48724019 1.01499462 -0.2723291 1.25395112 -0.332520192
## 393 -0.48724019 1.01499462 -0.2723291 1.25395112 -1.777119159
## 394 -0.48724019 1.01499462 -0.2723291 1.19354259 -0.130418661
## 395 -0.48724019 1.01499462 -0.2723291 1.19354259 -0.565933227
## 396 -0.48724019 1.01499462 -0.2723291 1.19354259 0.265244898
## 397 -0.48724019 1.01499462 -0.2723291 1.19354259 0.171310384
## 398 -0.48724019 1.01499462 -0.2723291 1.19354259 -0.765188257
## 399 -0.48724019 1.01499462 -0.2723291 1.19354259 -1.183623820
## 400 -0.48724019 1.01499462 -0.2723291 1.19354259 -0.615746985
## 401 -0.48724019 1.01499462 -0.2723291 1.19354259 -0.423608206
## 402 -0.48724019 1.01499462 -0.2723291 1.19354259 0.083068871
## 403 -0.48724019 1.01499462 -0.2723291 1.19354259 0.169887134
## 404 -0.48724019 1.01499462 -0.2723291 1.19354259 -1.331641842
## 405 -0.48724019 1.01499462 -0.2723291 1.19354259 -1.072610303
## 406 -0.48724019 1.01499462 -0.2723291 1.19354259 -0.856276271
## 407 -0.48724019 1.01499462 -0.2723291 0.90012973 -3.055197852
## 408 -0.48724019 1.01499462 -0.2723291 0.90012973 -0.963020037
## 409 -0.48724019 1.01499462 -0.2723291 0.36508275 -0.950210785
## 410 -0.48724019 1.01499462 -0.2723291 0.36508275 0.807503230
## 411 -0.48724019 1.01499462 -0.2723291 0.36508275 -0.750955755
## 412 -0.48724019 1.01499462 -0.2723291 0.36508275 0.529969438
## 413 -0.48724019 1.01499462 -0.2723291 0.36508275 -2.357805247
## 414 -0.48724019 1.01499462 -0.2723291 0.36508275 -1.607752384
## 415 -0.48724019 1.01499462 -0.2723291 1.19354259 -2.512939520
## 416 -0.48724019 1.01499462 -0.2723291 1.07272553 0.212584640
## 417 -0.48724019 1.01499462 -0.2723291 1.07272553 0.707875715
## 418 -0.48724019 1.01499462 -0.2723291 1.07272553 -1.395688102
## 419 -0.48724019 1.01499462 -0.2723291 1.07272553 -0.466305712
## 420 -0.48724019 1.01499462 -0.2723291 1.40928733 0.767652224
## 421 -0.48724019 1.01499462 -0.2723291 1.40928733 0.179849885
## 422 -0.48724019 1.01499462 -0.2723291 1.40928733 -0.396566452
## 423 -0.48724019 1.01499462 -0.2723291 0.51178918 -0.906090028
## 424 -0.48724019 1.01499462 -0.2723291 0.51178918 -0.258511181
## 425 -0.48724019 1.01499462 -0.2723291 0.25289548 -1.024219796
## 426 -0.48724019 1.01499462 -0.2723291 1.07272553 -0.553123975
## 427 -0.48724019 1.01499462 -0.2723291 0.25289548 -0.637095738
## 428 -0.48724019 1.01499462 -0.2723291 1.07272553 -0.117609410
## 429 -0.48724019 1.01499462 -0.2723291 1.07272553 -0.130418661
## 430 -0.48724019 1.01499462 -0.2723291 1.07272553 0.135729129
## 431 -0.48724019 1.01499462 -0.2723291 0.25289548 0.090185122
## 432 -0.48724019 1.01499462 -0.2723291 0.25289548 0.780461476
## 433 -0.48724019 1.01499462 -0.2723291 0.25289548 0.199775388
## 434 -0.48724019 1.01499462 -0.2723291 1.36613839 0.215431141
## 435 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.109069908
## 436 -0.48724019 1.01499462 -0.2723291 1.59914271 0.490118432
## 437 -0.48724019 1.01499462 -0.2723291 1.59914271 0.251012396
## 438 -0.48724019 1.01499462 -0.2723291 1.59914271 -0.188771920
## 439 -0.48724019 1.01499462 -0.2723291 1.59914271 -0.497617217
## 440 -0.48724019 1.01499462 -0.2723291 1.59914271 -0.935978283
## 441 -0.48724019 1.01499462 -0.2723291 1.59914271 -0.664137492
## 442 -0.48724019 1.01499462 -0.2723291 1.59914271 0.172733634
## 443 -0.48724019 1.01499462 -0.2723291 1.59914271 -0.093414156
## 444 -0.48724019 1.01499462 -0.2723291 1.59914271 0.285170401
## 445 -0.48724019 1.01499462 -0.2723291 1.59914271 -0.612900484
## 446 -0.48724019 1.01499462 -0.2723291 1.59914271 0.248165896
## 447 -0.48724019 1.01499462 -0.2723291 1.59914271 0.080222370
## 448 -0.48724019 1.01499462 -0.2723291 1.59914271 -0.047870149
## 449 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.141804663
## 450 -0.48724019 1.01499462 -0.2723291 1.36613839 0.188389387
## 451 -0.48724019 1.01499462 -0.2723291 1.36613839 0.660908458
## 452 -0.48724019 1.01499462 -0.2723291 1.36613839 0.527122938
## 453 -0.48724019 1.01499462 -0.2723291 1.36613839 0.017599361
## 454 -0.48724019 1.01499462 -0.2723291 1.36613839 1.577481596
## 455 -0.48724019 1.01499462 -0.2723291 1.36613839 0.631020203
## 456 -0.48724019 1.01499462 -0.2723291 1.36613839 0.342100410
## 457 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.439263958
## 458 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.496193967
## 459 -0.48724019 1.01499462 -0.2723291 1.36613839 0.023292362
## 460 -0.48724019 1.01499462 -0.2723291 1.36613839 -0.289822685
## 461 -0.48724019 1.01499462 -0.2723291 1.36613839 0.592592447
## 462 -0.48724019 1.01499462 -0.2723291 1.36613839 0.130036128
## 463 -0.48724019 1.01499462 -0.2723291 1.36613839 0.046064365
## 464 -0.48724019 1.01499462 -0.2723291 1.36613839 0.325021407
## 465 -0.48724019 1.01499462 -0.2723291 0.86561057 -0.107646658
## 466 -0.48724019 1.01499462 -0.2723291 0.86561057 -0.748109254
## 467 -0.48724019 1.01499462 -0.2723291 0.86561057 -0.473421963
## 468 -0.48724019 1.01499462 -0.2723291 0.25289548 -0.400836202
## 469 -0.48724019 1.01499462 -0.2723291 0.21837632 -0.510426469
## 470 -0.48724019 1.01499462 -0.2723291 0.21837632 -0.813578764
## 471 -0.48724019 1.01499462 -0.2723291 0.21837632 -0.167423167
## 472 -0.48724019 1.01499462 -0.2723291 -0.19585359 -0.079181654
## 473 -0.48724019 1.01499462 -0.2723291 0.21837632 0.216854391
## 474 -0.48724019 1.01499462 -0.2723291 0.51178918 0.989679257
## 475 -0.48724019 1.01499462 -0.2723291 0.25289548 -1.220628326
## 476 -0.48724019 1.01499462 -0.2723291 0.25289548 -0.174539418
## 477 -0.48724019 1.01499462 -0.2723291 0.51178918 0.283747151
## 478 -0.48724019 1.01499462 -0.2723291 0.51178918 -1.395688102
## 479 -0.48724019 1.01499462 -0.2723291 0.51178918 -0.141804663
## 480 -0.48724019 1.01499462 -0.2723291 0.51178918 -0.079181654
## 481 -0.48724019 1.01499462 -0.2723291 -0.19585359 -0.060679401
## 482 -0.48724019 1.01499462 -0.2723291 -0.19585359 0.662331708
## 483 -0.48724019 1.01499462 -0.2723291 -0.19585359 1.104962525
## 484 -0.48724019 1.01499462 -0.2723291 -0.19585359 -0.743839504
## 485 -0.48724019 1.01499462 -0.2723291 0.24426569 -0.588705230
## 486 -0.48724019 1.01499462 -0.2723291 0.24426569 0.038948114
## 487 -0.48724019 1.01499462 -0.2723291 0.24426569 -0.242855428
## 488 -0.48724019 1.01499462 -0.2723291 0.24426569 -0.540314723
## 489 -0.48724019 2.42017014 -0.2723291 0.46864023 -1.182200570
## 490 -0.48724019 2.42017014 -0.2723291 0.46864023 -1.239130578
## 491 -0.48724019 2.42017014 -0.2723291 0.46864023 -1.695993897
## 492 -0.48724019 2.42017014 -0.2723291 0.46864023 -0.429301206
## 493 -0.48724019 2.42017014 -0.2723291 0.46864023 -0.429301206
## 494 -0.48724019 -0.21088983 -0.2723291 0.26152527 -0.822118266
## 495 -0.48724019 -0.21088983 -0.2723291 0.26152527 -0.510426469
## 496 -0.48724019 -0.21088983 -0.2723291 0.26152527 -0.874778524
## 497 -0.48724019 -0.21088983 -0.2723291 0.26152527 -1.273288584
## 498 -0.48724019 -0.21088983 -0.2723291 0.26152527 -0.698295497
## 499 -0.48724019 -0.21088983 -0.2723291 0.26152527 -0.378064199
## 500 -0.48724019 -0.21088983 -0.2723291 0.26152527 -1.018526795
## 501 -0.48724019 -0.21088983 -0.2723291 0.26152527 -0.366678197
## 502 -0.48724019 0.11562398 -0.2723291 0.15796779 0.438881424
## 503 -0.48724019 0.11562398 -0.2723291 0.15796779 -0.234315927
## 504 -0.48724019 0.11562398 -0.2723291 0.15796779 0.983986256
## 505 -0.48724019 0.11562398 -0.2723291 0.15796779 0.724954717
## 506 -0.48724019 0.11562398 -0.2723291 0.15796779 -0.362408446
## age dis rad tax ptratio
## 1 -0.119894767 0.1400749840 -0.9818712 -0.66594918 -1.45755797
## 2 0.366803426 0.5566090496 -0.8670245 -0.98635338 -0.30279450
## 3 -0.265548971 0.5566090496 -0.8670245 -0.98635338 -0.30279450
## 4 -0.809087830 1.0766711351 -0.7521778 -1.10502160 0.11292035
## 5 -0.510674339 1.0766711351 -0.7521778 -1.10502160 0.11292035
## 6 -0.350809969 1.0766711351 -0.7521778 -1.10502160 0.11292035
## 7 -0.070159185 0.8384142195 -0.5224844 -0.57694801 -1.50374851
## 8 0.977840575 1.0236248974 -0.5224844 -0.57694801 -1.50374851
## 9 1.116389695 1.0861216287 -0.5224844 -0.57694801 -1.50374851
## 10 0.615481336 1.3283202075 -0.5224844 -0.57694801 -1.50374851
## 11 0.913894827 1.2117799501 -0.5224844 -0.57694801 -1.50374851
## 12 0.508905089 1.1547920492 -0.5224844 -0.57694801 -1.50374851
## 13 -1.050660656 0.7863652700 -0.5224844 -0.57694801 -1.50374851
## 14 -0.240681180 0.4333252240 -0.6373311 -0.60068166 1.17530274
## 15 0.565745754 0.3166899868 -0.6373311 -0.60068166 1.17530274
## 16 -0.428965883 0.3341187865 -0.6373311 -0.60068166 1.17530274
## 17 -1.395257187 0.3341187865 -0.6373311 -0.60068166 1.17530274
## 18 0.466274590 0.2198105553 -0.6373311 -0.60068166 1.17530274
## 19 -1.135921653 0.0006920764 -0.6373311 -0.60068166 1.17530274
## 20 0.032864520 0.0006920764 -0.6373311 -0.60068166 1.17530274
## 21 1.048891406 0.0013569352 -0.6373311 -0.60068166 1.17530274
## 22 0.732715207 0.1031753182 -0.6373311 -0.60068166 1.17530274
## 23 0.821528746 0.0863638874 -0.6373311 -0.60068166 1.17530274
## 24 1.116389695 0.1425444597 -0.6373311 -0.60068166 1.17530274
## 25 0.906789743 0.2871037683 -0.6373311 -0.60068166 1.17530274
## 26 0.608376252 0.3132232229 -0.6373311 -0.60068166 1.17530274
## 27 0.771793164 0.4212152950 -0.6373311 -0.60068166 1.17530274
## 28 0.718505041 0.3126533438 -0.6373311 -0.60068166 1.17530274
## 29 0.917447368 0.3132707128 -0.6373311 -0.60068166 1.17530274
## 30 0.665216917 0.2108349609 -0.6373311 -0.60068166 1.17530274
## 31 0.906789743 0.2079855659 -0.6373311 -0.60068166 1.17530274
## 32 1.116389695 0.1804414138 -0.6373311 -0.60068166 1.17530274
## 33 0.476932215 0.0925850666 -0.6373311 -0.60068166 1.17530274
## 34 0.938762618 -0.0037244859 -0.6373311 -0.60068166 1.17530274
## 35 1.006260907 -0.0167367233 -0.6373311 -0.60068166 1.17530274
## 36 -0.013318520 -0.2064589434 -0.5224844 -0.76681717 0.34387304
## 37 -0.254891346 -0.1981007179 -0.5224844 -0.76681717 0.34387304
## 38 -0.961847117 0.0660856927 -0.5224844 -0.76681717 0.34387304
## 39 -1.363284313 0.0248169544 -0.5224844 -0.76681717 0.34387304
## 40 -1.661697804 0.7627152911 -0.7521778 -0.92701927 -0.07184181
## 41 -1.874850298 0.7627152911 -0.7521778 -0.92701927 -0.07184181
## 42 -2.333128159 0.9145880470 -0.7521778 -1.03975408 -0.25660396
## 43 -2.201684121 0.9145880470 -0.7521778 -1.03975408 -0.25660396
## 44 -2.205236663 0.9145880470 -0.7521778 -1.03975408 -0.25660396
## 45 -1.015135240 0.9145880470 -0.7521778 -1.03975408 -0.25660396
## 46 -1.235392817 0.6199131095 -0.7521778 -1.03975408 -0.25660396
## 47 -1.253155525 0.6199131095 -0.7521778 -1.03975408 -0.25660396
## 48 0.601271169 0.8996287230 -0.7521778 -1.03975408 -0.25660396
## 49 0.949420242 0.9853955139 -0.7521778 -1.03975408 -0.25660396
## 50 -0.233576097 1.0887810641 -0.7521778 -1.03975408 -0.25660396
## 51 -0.812640371 1.4340327636 -0.6373311 -0.98041997 -0.76469989
## 52 -0.198050682 1.4340327636 -0.6373311 -0.98041997 -0.76469989
## 53 -1.686565595 1.4340327636 -0.6373311 -0.98041997 -0.76469989
## 54 -1.675907970 1.4340327636 -0.6373311 -0.98041997 -0.76469989
## 55 -0.745142082 1.6738568465 -0.7521778 0.36053095 1.22149328
## 56 -1.658145262 2.3277455193 -0.5224844 -1.08128796 -0.25660396
## 57 -1.167894527 2.5609210138 -0.8670245 -0.56508119 -0.53374719
## 58 -0.997372532 2.1511780064 -0.5224844 -0.90328562 -1.54993904
## 59 -1.398809729 1.9089794276 -0.1779443 -0.73715011 0.57482574
## 60 -0.759352248 1.4897384367 -0.1779443 -0.73715011 0.57482574
## 61 -0.084369352 1.6290738544 -0.1779443 -0.73715011 0.57482574
## 62 0.881921953 1.4358373805 -0.1779443 -0.73715011 0.57482574
## 63 -0.027528687 1.6291213443 -0.1779443 -0.73715011 0.57482574
## 64 -0.894348827 1.9878601804 -0.1779443 -0.73715011 0.57482574
## 65 -0.322389636 2.5776849546 -0.7521778 -1.14062207 0.06672981
## 66 -1.803799466 1.3375332514 -0.6373311 -0.42267932 -1.08803366
## 67 -1.331311439 1.3375332514 -0.6373311 -0.42267932 -1.08803366
## 68 -1.675907970 1.2836321952 -0.6373311 -0.37521203 0.20530143
## 69 -1.128816570 1.2836321952 -0.6373311 -0.37521203 0.20530143
## 70 -1.263813149 1.2836321952 -0.6373311 -0.37521203 0.20530143
## 71 -2.201684121 0.7086717651 -0.6373311 -0.61254848 0.34387304
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## 299 -1.722091011 1.9151531169 -0.5224844 -0.29807769 -1.68851066
## 300 -2.080897708 1.9151531169 -0.5224844 -0.29807769 -1.68851066
## 301 -0.752247165 1.9151531169 -0.5224844 -0.29807769 -1.68851066
## 302 -1.000925074 0.8057411563 -0.2927910 -0.47014661 -1.08803366
## 303 -1.782484217 0.8057411563 -0.2927910 -0.47014661 -1.08803366
## 304 -1.807352008 0.8057411563 -0.2927910 -0.47014661 -1.08803366
## 305 -0.976057283 0.1077818401 -0.2927910 -1.10502160 -0.02565127
## 306 -0.372125218 -0.2018524214 -0.2927910 -1.10502160 -0.02565127
## 307 0.118125517 -0.3304551177 -0.2927910 -1.10502160 -0.02565127
## 308 0.061284852 -0.2908010367 -0.2927910 -1.10502160 -0.02565127
## 309 0.494694923 -0.2267846280 -0.6373311 -0.61848189 -0.02565127
## 310 0.288647512 -0.3288879504 -0.6373311 -0.61848189 -0.02565127
## 311 -1.093291155 -0.6058016588 -0.6373311 -0.61848189 -0.02565127
## 312 -0.560409921 -0.5483863487 -0.6373311 -0.61848189 -0.02565127
## 313 0.775345706 -0.4563983787 -0.6373311 -0.61848189 -0.02565127
## 314 0.505352547 -0.2527616128 -0.6373311 -0.61848189 -0.02565127
## 315 0.665216917 -0.0915333432 -0.6373311 -0.61848189 -0.02565127
## 316 0.324172928 0.0712146037 -0.6373311 -0.61848189 -0.02565127
## 317 0.519562713 0.0966691995 -0.6373311 -0.61848189 -0.02565127
## 318 0.111020434 0.1123883621 -0.6373311 -0.61848189 -0.02565127
## 319 -0.048843936 -0.1246813056 -0.6373311 -0.61848189 -0.02565127
## 320 -0.347257427 0.0982363667 -0.6373311 -0.61848189 -0.02565127
## 321 -0.578172628 0.3539695720 -0.5224844 -0.71934988 0.52863520
## 322 -0.507121797 0.3539695720 -0.5224844 -0.71934988 0.52863520
## 323 -0.663433626 0.4397838527 -0.5224844 -0.71934988 0.52863520
## 324 0.203386515 0.4397838527 -0.5224844 -0.71934988 0.52863520
## 325 -1.011582699 0.4397838527 -0.5224844 -0.71934988 0.52863520
## 326 -1.913928255 0.7697437989 -0.5224844 -0.71934988 0.52863520
## 327 -1.409467353 0.7697437989 -0.5224844 -0.71934988 0.52863520
## 328 -0.883691203 0.7697437989 -0.5224844 -0.71934988 0.52863520
## 329 -1.519596142 0.6741465952 -0.6373311 0.12912791 -0.71850935
## 330 -1.825114716 0.6741465952 -0.6373311 0.12912791 -0.71850935
## 331 -1.292233482 0.9871051509 -0.6373311 0.12912791 -0.71850935
## 332 -1.427230061 1.3514003073 -0.9818712 -0.61848189 -0.71850935
## 333 -1.608409681 1.3514003073 -0.9818712 -0.61848189 -0.71850935
## 334 -1.082633530 1.2648261879 -0.5224844 -1.09315478 0.80577843
## 335 -1.068423364 1.2648261879 -0.5224844 -1.09315478 0.80577843
## 336 -1.210525026 1.0401513886 -0.5224844 -1.09315478 0.80577843
## 337 -0.791325122 0.6819824315 -0.5224844 -1.09315478 0.80577843
## 338 -0.318837095 0.8642962245 -0.5224844 -1.09315478 0.80577843
## 339 -1.111053862 0.4830471675 -0.5224844 -1.09315478 0.80577843
## 340 -0.823297996 0.4830471675 -0.5224844 -1.09315478 0.80577843
## 341 -0.357915052 0.4830471675 -0.5224844 -1.09315478 0.80577843
## 342 -0.684748875 1.5400302593 -0.9818712 -0.73715011 -1.36517689
## 343 -0.315284553 1.1738829960 -0.9818712 0.08166062 -1.18041474
## 344 -0.432518424 0.9199069177 -0.5224844 -0.22687676 -0.39517558
## 345 -1.437887686 1.2681504821 -0.5224844 -0.22687676 -0.39517558
## 346 -0.713169208 2.0033893834 -0.7521778 -0.33367816 0.15911089
## 347 -0.578172628 2.0033893834 -0.7521778 -0.33367816 0.15911089
## 348 -1.452097852 2.2511442825 -0.6373311 -0.33961157 -0.25660396
## 349 -1.381047021 2.1602960705 -0.6373311 -0.76088376 -0.67231881
## 350 -1.210525026 2.3730983904 -0.9818712 -0.43454615 0.57482574
## 351 -0.858823412 2.3730983904 -0.9818712 -0.43454615 0.57482574
## 352 -1.160789444 3.2840499862 -0.6373311 0.01639310 -0.07184181
## 353 -1.778931675 3.2840499862 -0.6373311 0.01639310 -0.07184181
## 354 -1.153684361 3.9566021965 -0.5224844 -1.31269099 -0.67231881
## 355 -1.658145262 3.2248775491 -0.6373311 -0.44047956 1.63720813
## 356 -1.743406260 3.2248775491 -0.6373311 -0.44047956 1.63720813
## 357 1.024023615 -0.7944316108 1.6596029 1.52941294 0.80577843
## 358 0.796660955 -0.6125452271 1.6596029 1.52941294 0.80577843
## 359 0.526667797 -0.5092546567 1.6596029 1.52941294 0.80577843
## 360 0.452064424 -0.6106931203 1.6596029 1.52941294 0.80577843
## 361 0.690084708 -0.6063715378 1.6596029 1.52941294 0.80577843
## 362 0.800213497 -0.7121315839 1.6596029 1.52941294 0.80577843
## 363 0.981393116 -0.8032647354 1.6596029 1.52941294 0.80577843
## 364 0.725610124 -0.8977221812 1.6596029 1.52941294 0.80577843
## 365 0.508905089 -0.8977221812 1.6596029 1.52941294 0.80577843
## 366 0.686532167 -1.0361552904 1.6596029 1.52941294 0.80577843
## 367 0.810871121 -0.9700968153 1.6596029 1.52941294 0.80577843
## 368 1.116389695 -1.0848799457 1.6596029 1.52941294 0.80577843
## 369 1.116389695 -1.1694594886 1.6596029 1.52941294 0.80577843
## 370 1.002708366 -1.1579669285 1.6596029 1.52941294 0.80577843
## 371 1.027576156 -1.2312438711 1.6596029 1.52941294 0.80577843
## 372 1.116389695 -1.2470580136 1.6596029 1.52941294 0.80577843
## 373 0.746925373 -1.2658165310 1.6596029 1.52941294 0.80577843
## 374 1.116389695 -1.2446360278 1.6596029 1.52941294 0.80577843
## 375 1.116389695 -1.2623022771 1.6596029 1.52941294 0.80577843
## 376 1.041786323 -1.1771528552 1.6596029 1.52941294 0.80577843
## 377 0.878369411 -1.1635707388 1.6596029 1.52941294 0.80577843
## 378 1.073759197 -1.1573495596 1.6596029 1.52941294 0.80577843
## 379 0.981393116 -1.1440048928 1.6596029 1.52941294 0.80577843
## 380 1.116389695 -1.1440048928 1.6596029 1.52941294 0.80577843
## 381 0.828633829 -1.1295679579 1.6596029 1.52941294 0.80577843
## 382 1.084416821 -1.0807958128 1.6596029 1.52941294 0.80577843
## 383 1.116389695 -1.0517319833 1.6596029 1.52941294 0.80577843
## 384 1.116389695 -1.0741947142 1.6596029 1.52941294 0.80577843
## 385 0.803766038 -1.1186452769 1.6596029 1.52941294 0.80577843
## 386 1.048891406 -1.1250089259 1.6596029 1.52941294 0.80577843
## 387 1.116389695 -1.1054905698 1.6596029 1.52941294 0.80577843
## 388 0.743372832 -1.0811757321 1.6596029 1.52941294 0.80577843
## 389 1.116389695 -1.0474104008 1.6596029 1.52941294 0.80577843
## 390 1.077311738 -0.9815893753 1.6596029 1.52941294 0.80577843
## 391 1.009813449 -0.8873693792 1.6596029 1.52941294 0.80577843
## 392 0.494694923 -0.7727762084 1.6596029 1.52941294 0.80577843
## 393 1.009813449 -0.9616910999 1.6596029 1.52941294 0.80577843
## 394 0.853501620 -0.9516232374 1.6596029 1.52941294 0.80577843
## 395 0.928104993 -0.9559448199 1.6596029 1.52941294 0.80577843
## 396 1.073759197 -0.9827291333 1.6596029 1.52941294 0.80577843
## 397 0.974288033 -1.0059517029 1.6596029 1.52941294 0.80577843
## 398 1.077311738 -1.0265623271 1.6596029 1.52941294 0.80577843
## 399 1.116389695 -1.0948528283 1.6596029 1.52941294 0.80577843
## 400 0.327725469 -1.0897239172 1.6596029 1.52941294 0.80577843
## 401 1.116389695 -1.0477428302 1.6596029 1.52941294 0.80577843
## 402 1.116389695 -1.0547238481 1.6596029 1.52941294 0.80577843
## 403 1.116389695 -1.0239028917 1.6596029 1.52941294 0.80577843
## 404 0.974288033 -0.9936043244 1.6596029 1.52941294 0.80577843
## 405 0.597718628 -1.0389097056 1.6596029 1.52941294 0.80577843
## 406 1.116389695 -1.1253413553 1.6596029 1.52941294 0.80577843
## 407 1.116389695 -1.2427839210 1.6596029 1.52941294 0.80577843
## 408 1.116389695 -1.1919222195 1.6596029 1.52941294 0.80577843
## 409 1.041786323 -1.1114268095 1.6596029 1.52941294 0.80577843
## 410 1.116389695 -1.1062978984 1.6596029 1.52941294 0.80577843
## 411 1.116389695 -1.1312301050 1.6596029 1.52941294 0.80577843
## 412 1.116389695 -1.0768541496 1.6596029 1.52941294 0.80577843
## 413 1.116389695 -1.0643168114 1.6596029 1.52941294 0.80577843
## 414 1.116389695 -1.0474578907 1.6596029 1.52941294 0.80577843
## 415 1.116389695 -1.0147848276 1.6596029 1.52941294 0.80577843
## 416 1.116389695 -0.9309651233 1.6596029 1.52941294 0.80577843
## 417 0.789555872 -0.9381835908 1.6596029 1.52941294 0.80577843
## 418 0.729162665 -1.0198662487 1.6596029 1.52941294 0.80577843
## 419 1.116389695 -0.9462093868 1.6596029 1.52941294 0.80577843
## 420 0.281542429 -0.9502935197 1.6596029 1.52941294 0.80577843
## 421 1.116389695 -0.9194725633 1.6596029 1.52941294 0.80577843
## 422 0.949420242 -0.9120166463 1.6596029 1.52941294 0.80577843
## 423 0.675874542 -0.8756393696 1.6596029 1.52941294 0.80577843
## 424 0.587061003 -0.8421114879 1.6596029 1.52941294 0.80577843
## 425 0.071942477 -0.8223081923 1.6596029 1.52941294 0.80577843
## 426 0.952972784 -0.8953951752 1.6596029 1.52941294 0.80577843
## 427 -0.315284553 -0.8536040479 1.6596029 1.52941294 0.80577843
## 428 0.359698343 -0.9175729666 1.6596029 1.52941294 0.80577843
## 429 0.338383094 -0.8830477967 1.6596029 1.52941294 0.80577843
## 430 0.960077867 -0.8675660836 1.6596029 1.52941294 0.80577843
## 431 0.622586419 -0.8274371034 1.6596029 1.52941294 0.80577843
## 432 0.913894827 -0.8105781827 1.6596029 1.52941294 0.80577843
## 433 0.221149222 -0.7572944954 1.6596029 1.52941294 0.80577843
## 434 0.686532167 -0.7024911307 1.6596029 1.52941294 0.80577843
## 435 0.938762618 -0.7469416934 1.6596029 1.52941294 0.80577843
## 436 0.924552451 -0.7932443629 1.6596029 1.52941294 0.80577843
## 437 0.878369411 -0.8512295520 1.6596029 1.52941294 0.80577843
## 438 1.116389695 -0.8932106390 1.6596029 1.52941294 0.80577843
## 439 0.686532167 -0.9376612017 1.6596029 1.52941294 0.80577843
## 440 0.899684660 -0.9392758589 1.6596029 1.52941294 0.80577843
## 441 0.846396537 -0.9160057994 1.6596029 1.52941294 0.80577843
## 442 1.016918532 -0.8215483536 1.6596029 1.52941294 0.80577843
## 443 1.116389695 -0.8501847738 1.6596029 1.52941294 0.80577843
## 444 1.116389695 -0.8627221120 1.6596029 1.52941294 0.80577843
## 445 0.995603282 -0.9020437636 1.6596029 1.52941294 0.80577843
## 446 0.931657534 -0.8582105699 1.6596029 1.52941294 0.80577843
## 447 0.988498199 -0.8182715493 1.6596029 1.52941294 0.80577843
## 448 0.995603282 -0.7584342534 1.6596029 1.52941294 0.80577843
## 449 1.070206655 -0.7282306659 1.6596029 1.52941294 0.80577843
## 450 1.055996489 -0.7646079427 1.6596029 1.52941294 0.80577843
## 451 0.853501620 -0.6987869171 1.6596029 1.52941294 0.80577843
## 452 1.052443947 -0.6837801032 1.6596029 1.52941294 0.80577843
## 453 0.825081288 -0.6776064140 1.6596029 1.52941294 0.80577843
## 454 1.091521905 -0.6374774338 1.6596029 1.52941294 0.80577843
## 455 0.906789743 -0.6168668096 1.6596029 1.52941294 0.80577843
## 456 0.636796585 -0.6455032298 1.6596029 1.52941294 0.80577843
## 457 0.686532167 -0.5767378294 1.6596029 1.52941294 0.80577843
## 458 0.416539008 -0.4824228534 1.6596029 1.52941294 0.80577843
## 459 0.537325421 -0.4805707466 1.6596029 1.52941294 0.80577843
## 460 0.562193212 -0.5117241325 1.6596029 1.52941294 0.80577843
## 461 0.761135540 -0.5687120333 1.6596029 1.52941294 0.80577843
## 462 0.704294875 -0.5831489682 1.6596029 1.52941294 0.80577843
## 463 0.512457630 -0.5036983364 1.6596029 1.52941294 0.80577843
## 464 0.757582998 -0.4717851119 1.6596029 1.52941294 0.80577843
## 465 -0.112789684 -0.3949464255 1.6596029 1.52941294 0.80577843
## 466 -0.723826832 -0.3459843207 1.6596029 1.52941294 0.80577843
## 467 0.572850837 -0.4385896596 1.6596029 1.52941294 0.80577843
## 468 0.920999910 -0.5958762661 1.6596029 1.52941294 0.80577843
## 469 0.086152643 -0.4210658801 1.6596029 1.52941294 0.80577843
## 470 -0.421860800 -0.4612898402 1.6596029 1.52941294 0.80577843
## 471 0.547983046 -0.3617034834 1.6596029 1.52941294 0.80577843
## 472 0.786003330 -0.3304076278 1.6596029 1.52941294 0.80577843
## 473 0.228254306 -0.4267171803 1.6596029 1.52941294 0.80577843
## 474 -0.034633770 -0.5993905200 1.6596029 1.52941294 0.80577843
## 475 0.952972784 -0.6483526248 1.6596029 1.52941294 0.80577843
## 476 1.024023615 -0.7546350600 1.6596029 1.52941294 0.80577843
## 477 0.889027036 -0.7074775720 1.6596029 1.52941294 0.80577843
## 478 1.020471073 -0.8046419430 1.6596029 1.52941294 0.80577843
## 479 0.999155824 -0.7714939807 1.6596029 1.52941294 0.80577843
## 480 0.690084708 -0.8756393696 1.6596029 1.52941294 0.80577843
## 481 -0.137657475 -0.1761128861 1.6596029 1.52941294 0.80577843
## 482 0.224701764 -0.2200410597 1.6596029 1.52941294 0.80577843
## 483 0.299305137 -0.1825715149 1.6596029 1.52941294 0.80577843
## 484 -1.004477616 0.1440166471 1.6596029 1.52941294 0.80577843
## 485 -0.947636951 -0.0337381137 1.6596029 1.52941294 0.80577843
## 486 -0.592382795 0.0933923952 1.6596029 1.52941294 0.80577843
## 487 0.398776300 -0.1183176566 1.6596029 1.52941294 0.80577843
## 488 -0.546199754 -0.3052379716 1.6596029 1.52941294 0.80577843
## 489 0.857054162 -0.9375187319 -0.6373311 1.79641644 0.75958789
## 490 1.055996489 -0.9686246278 -0.6373311 1.79641644 0.75958789
## 491 1.045338864 -0.9367114033 -0.6373311 1.79641644 0.75958789
## 492 1.073759197 -0.9151034909 -0.6373311 1.79641644 0.75958789
## 493 0.530220338 -0.8002728706 -0.6373311 1.79641644 0.75958789
## 494 -0.517779422 -0.6711952751 -0.4076377 -0.10227512 0.34387304
## 495 -0.922769160 -0.6711952751 -0.4076377 -0.10227512 0.34387304
## 496 -1.413019895 -0.4732098094 -0.4076377 -0.10227512 0.34387304
## 497 0.153650933 -0.4732098094 -0.4076377 -0.10227512 0.34387304
## 498 0.071942477 -0.4285217972 -0.4076377 -0.10227512 0.34387304
## 499 -0.116342226 -0.6581830377 -0.4076377 -0.10227512 0.34387304
## 500 0.174966182 -0.6625521101 -0.4076377 -0.10227512 0.34387304
## 501 0.395223759 -0.6158695213 -0.4076377 -0.10227512 0.34387304
## 502 0.018654354 -0.6251775451 -0.9818712 -0.80241764 1.17530274
## 503 0.288647512 -0.7159307773 -0.9818712 -0.80241764 1.17530274
## 504 0.796660955 -0.7729186782 -0.9818712 -0.80241764 1.17530274
## 505 0.736267749 -0.6677760011 -0.9818712 -0.80241764 1.17530274
## 506 0.434301716 -0.6126402069 -0.9818712 -0.80241764 1.17530274
## black lstat medv
## 1 0.440615895 -1.074498970 0.159527789
## 2 0.440615895 -0.491952525 -0.101423917
## 3 0.396035074 -1.207532413 1.322937477
## 4 0.415751408 -1.360170785 1.181588636
## 5 0.440615895 -1.025486649 1.486032293
## 6 0.410165113 -1.042290874 0.670558212
## 7 0.426376321 -0.031236706 0.039924923
## 8 0.440615895 0.909799859 0.496590409
## 9 0.328123258 2.419379350 -0.655946292
## 10 0.328999540 0.622727693 -0.394994586
## 11 0.392639483 1.091845624 -0.819041108
## 12 0.440615895 0.086392864 -0.394994586
## 13 0.370513376 0.428078760 -0.090550930
## 14 0.440615895 -0.615183504 -0.231899770
## 15 0.255720500 -0.335113097 -0.471105500
## 16 0.426595391 -0.585776111 -0.286264709
## 17 0.330533033 -0.850442645 0.061670899
## 18 0.329437681 0.282442149 -0.547216415
## 19 -0.741378303 -0.134862757 -0.253645746
## 20 0.375442459 -0.192277190 -0.471105500
## 21 0.217930861 1.171665689 -0.971262937
## 22 0.392749018 0.164812578 -0.318883672
## 23 0.440615895 0.849584722 -0.797295133
## 24 0.414765591 1.012025558 -0.873406047
## 25 0.412465352 0.510699530 -0.753803182
## 26 -0.583319029 0.540106923 -0.938643973
## 27 0.221326452 0.302047077 -0.645073304
## 28 -0.550896614 0.647934029 -0.840787084
## 29 0.342472368 0.020576319 -0.449359525
## 30 0.258020739 -0.094252548 -0.166661844
## 31 0.038293155 1.392921311 -1.069119826
## 32 0.219683424 0.054184768 -0.873406047
## 33 -1.359047220 2.108501199 -1.014754888
## 34 0.022958229 0.797771697 -1.025627875
## 35 -1.186967442 1.076441751 -0.982135924
## 36 0.440615895 -0.416333515 -0.394994586
## 37 0.228774844 -0.174072614 -0.275391721
## 38 0.440615895 -0.543765550 -0.166661844
## 39 0.402607185 -0.353317674 0.235638703
## 40 0.426704926 -1.166922204 0.898890955
## 41 0.426595391 -1.494604580 1.344683452
## 42 0.314759966 -1.094103899 0.442225470
## 43 0.292414788 -0.958269752 0.300876629
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## 402 0.440615895 1.073641047 -1.667134152
## 403 0.212892242 1.072240695 -1.134357753
## 404 0.440615895 0.996621685 -1.547531287
## 405 -0.298089403 2.062289582 -1.525785311
## 406 0.309940417 1.446134688 -1.906339882
## 407 0.148376017 1.496547361 -1.156103728
## 408 -0.269281649 -0.073247267 0.583574310
## 409 -0.460420549 1.925055083 -0.579835378
## 410 -1.942212553 0.998022037 0.540082359
## 411 -3.878356510 -0.356118378 -0.819041108
## 412 -3.522914830 1.199672730 -0.579835378
## 413 -3.591483857 3.041135653 -0.503724464
## 414 -1.595971828 1.040032598 -0.677692268
## 415 -2.939968567 3.406627533 -1.688880128
## 416 -3.608352275 2.296148371 -1.667134152
## 417 -3.670568261 1.839633609 -1.634515189
## 418 -2.511795523 1.958663532 -1.319198544
## 419 -3.726650277 1.115651608 -1.493166348
## 420 -3.376137680 1.412526239 -1.536658299
## 421 -0.415401588 0.331454470 -0.634200317
## 422 -0.401928760 0.426678408 -0.906025010
## 423 -0.713337295 0.202622083 -0.188407819
## 424 -3.879232792 1.489545601 -0.993008912
## 425 -3.866855315 0.631129805 -1.177849704
## 426 -3.822712635 1.643584324 -1.547531287
## 427 -3.636831424 0.425278056 -1.340944520
## 428 -3.700690438 0.261436868 -1.264833606
## 429 -2.847301799 1.241683291 -1.253960618
## 430 -3.241738006 1.600173411 -1.417055434
## 431 -2.992764527 0.698346703 -0.873406047
## 432 -3.015985986 0.985418869 -0.916897998
## 433 -2.833938506 -0.087250788 -0.699438243
## 434 -2.809402625 0.499496714 -0.895152022
## 435 -2.804583076 0.352459751 -1.177849704
## 436 -2.703591634 1.486744897 -0.993008912
## 437 -3.605723431 0.755761136 -1.406182446
## 438 -3.804748865 1.932056843 -1.504039336
## 439 -3.151590547 2.992123331 -1.536658299
## 440 0.440615895 1.432131167 -1.058246839
## 441 0.380919218 1.324304061 -1.308325557
## 442 0.320784401 0.961612885 -0.590708366
## 443 0.427362137 0.551309739 -0.449359525
## 444 0.329218610 0.867789298 -0.775549157
## 445 -1.272295352 1.559563202 -1.275706593
## 446 -3.435177145 1.586169891 -1.166976716
## 447 -0.423507192 0.719351983 -0.829914096
## 448 0.348825409 0.530304459 -1.079992814
## 449 0.440615895 0.766963952 -0.916897998
## 450 -0.574665749 0.932205492 -1.036500863
## 451 -3.903330533 0.670339662 -0.993008912
## 452 -0.015160016 0.710949871 -0.797295133
## 453 0.311254840 0.646533677 -0.699438243
## 454 0.210263398 0.572315020 -0.514597451
## 455 -3.833666154 0.848184370 -0.829914096
## 456 -3.349082489 0.766963952 -0.916897998
## 457 -3.792042783 0.890194931 -1.069119826
## 458 -3.868498343 0.600322060 -0.982135924
## 459 -0.925178346 0.500897066 -0.829914096
## 460 0.440615895 0.286643205 -0.275391721
## 461 -1.111169093 0.527503755 -0.666819280
## 462 0.380700148 0.279641445 -0.525470439
## 463 0.440615895 0.187218211 -0.329756660
## 464 0.406879058 -0.330912041 -0.253645746
## 465 0.440615895 0.079391104 -0.123169893
## 466 -0.243979021 0.206823139 -0.286264709
## 467 -3.665748713 0.629729453 -0.384121599
## 468 -0.278044464 1.213676250 -0.373248611
## 469 0.132164810 0.766963952 -0.373248611
## 470 0.440615895 0.295045317 -0.264518733
## 471 0.440615895 0.509299178 -0.286264709
## 472 0.423418871 0.030378783 -0.318883672
## 473 0.401949974 0.239031236 0.072543887
## 474 0.197228711 -0.139063813 0.790161078
## 475 -0.044844052 0.768364304 -0.949516961
## 476 -0.590548351 1.602974115 -1.003881900
## 477 0.433057967 0.843983314 -0.634200317
## 478 -0.078799960 1.716402630 -1.145230740
## 479 0.252215374 0.752960432 -0.862533059
## 480 0.291867112 0.063987232 -0.123169893
## 481 0.440615895 -0.267896200 0.050797911
## 482 0.398663919 -0.688001809 0.126908825
## 483 0.422871195 -0.790227508 0.268257666
## 484 0.397020891 -0.312707465 -0.079677942
## 485 0.153962312 0.096195329 -0.210153795
## 486 0.349920761 -0.290301832 -0.144915868
## 487 0.394392046 0.325853062 -0.373248611
## 488 0.345539353 -0.168471205 -0.210153795
## 489 0.420790026 0.757161488 -0.797295133
## 490 -0.138277566 1.584769539 -1.688880128
## 491 -0.418906714 2.384370549 -1.569277262
## 492 0.366241503 0.758561840 -0.971262937
## 493 0.440615895 0.097595681 -0.264518733
## 494 0.440615895 -0.090051492 -0.079677942
## 495 0.440615895 0.131204129 0.213892727
## 496 0.401073693 0.692745294 0.061670899
## 497 0.440615895 1.188469914 -0.308010684
## 498 0.440615895 0.202622083 -0.460232513
## 499 0.440615895 0.037380543 -0.144915868
## 500 0.428238419 0.342657286 -0.547216415
## 501 0.440615895 0.234830180 -0.623327329
## 502 0.386834118 -0.417733867 -0.014440015
## 503 0.440615895 -0.500354637 -0.210153795
## 504 0.440615895 -0.982075736 0.148654801
## 505 0.402826256 -0.864446166 -0.057931966
## 506 0.440615895 -0.668396881 -1.156103728boston_scaled<-data.frame(boston_scaled, crime)Divide the dataset into train and test
n<-nrow(boston_scaled)
ind<-sample(n, size = n*0.8)
train<-boston_scaled[ind, ]
test<-boston_scaled[-ind, ]
correct_classes<-test$crimeLinear Discriminant Analysis
lda.fit<-lda(crime~., data=train)
lda.fit## Call:
## lda(crime ~ ., data = train)
##
## Prior probabilities of groups:
## low med_low med_high high
## 0.2450495 0.2747525 0.2351485 0.2450495
##
## Group means:
## zn indus chas nox rm
## low 0.87075235 -0.8612966 -0.07348562 -0.8542804 0.4127885
## med_low -0.08821242 -0.2923476 0.01142590 -0.5625108 -0.1301879
## med_high -0.35906012 0.1541520 0.18354570 0.3596324 0.1037884
## high -0.48724019 1.0171737 -0.03371693 1.1004455 -0.4392496
## age dis rad tax ptratio
## low -0.8595770 0.8624144 -0.6918543 -0.7471590 -0.38817701
## med_low -0.3703329 0.3654480 -0.5473161 -0.4770957 -0.07100954
## med_high 0.4007956 -0.3845586 -0.4209357 -0.3293062 -0.30619801
## high 0.8024383 -0.8284699 1.6375616 1.5136504 0.78011702
## black lstat medv
## low 0.3812257 -0.74900907 0.49691989
## med_low 0.3221067 -0.13949275 0.02395828
## med_high 0.1037514 0.07056152 0.15952779
## high -0.7418906 0.87211766 -0.69713185
##
## Coefficients of linear discriminants:
## LD1 LD2 LD3
## zn 0.07430630 0.6739413323 -1.0503003
## indus 0.06577009 -0.1655276720 0.1665862
## chas -0.09327788 -0.0164629386 0.1402870
## nox 0.39369334 -0.8011409088 -1.3236015
## rm -0.06386765 -0.1076562202 -0.1896987
## age 0.22634748 -0.3139933045 -0.1162417
## dis -0.02506278 -0.1964260098 0.1669998
## rad 3.38034484 0.9291448260 -0.1167412
## tax 0.03411753 -0.0184446646 0.6865095
## ptratio 0.07358559 0.0765276095 -0.2617097
## black -0.08404990 0.0002793718 0.1145223
## lstat 0.23707185 -0.2793616534 0.3207011
## medv 0.19738866 -0.4312337227 -0.1689729
##
## Proportion of trace:
## LD1 LD2 LD3
## 0.9576 0.0309 0.0115lda.arrows<-function(x, myscale=1, arrow_heads= 0.1, color="red", tex=0.75, choices =c (1,2)){
heads<-coef(x)
arrows(x0 = 0, y0=0, x1 = myscale*heads[,choices[1]],y1=myscale*heads[,choices[2]], col=color, length= arrow_heads)
text(myscale * heads[,choices], labels = row.names(heads),
cex = tex, col=color, pos=3)
}Convert target classes to numeric data
classes<-as.numeric(train$crime)Plot the lda results
plot(lda.fit, dimen=2, col=classes, pch=classes)
lda.arrows(lda.fit, myscale=1)
Predict the classes with the LDA model and Cross-tabulate the results
lda.pred<-predict(lda.fit, newdata = test)
table(correct=correct_classes, predict=lda.pred$class)## predict
## correct low med_low med_high high
## low 17 11 0 0
## med_low 1 13 1 0
## med_high 0 13 16 2
## high 0 0 0 28Distance measures
library(MASS)
data("Boston")
boston_scaled<-scale(Boston)
boston_scaled<-as.data.frame(boston_scaled)Euclidean distane matrix
dist_eu<-dist(boston_scaled)
summary(dist_eu)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1343 3.4625 4.8241 4.9111 6.1863 14.3970K-means
km<-kmeans(boston_scaled, centers=3)
pairs(boston_scaled, col=km$cluster)
Investigate the optimal number of clusters
set.seed(11)
k_max<-20
twcss <- sapply(1:k_max, function(k){kmeans(boston_scaled, k)$tot.withinss})
qqplot(x=1:k_max, y = twcss, geom="Line")## Warning in plot.window(...): "geom" is not a graphical parameter## Warning in plot.xy(xy, type, ...): "geom" is not a graphical parameter## Warning in axis(side = side, at = at, labels = labels, ...): "geom" is not
## a graphical parameter
## Warning in axis(side = side, at = at, labels = labels, ...): "geom" is not
## a graphical parameter## Warning in box(...): "geom" is not a graphical parameter## Warning in title(...): "geom" is not a graphical parameter
Perform k-means with different number of clusters
km<-kmeans(boston_scaled, centers=6)
pairs(boston_scaled, col = km$cluster)
library(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2##
## Attaching package: 'GGally'## The following object is masked from 'package:dplyr':
##
## nasaggpairs(boston_scaled)
Super Bonus
model_predictors<- dplyr::select(train, -crime)Check th dimensions
dim(model_predictors)## [1] 404 13dim(lda.fit$scaling)## [1] 13 3Matrix multiplication
matrix_product <- as.matrix(model_predictors)%*%lda.fit$scaling
matrix_product <- as.data.frame(matrix_product)Create a 3D plot
library(plotly)##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:MASS':
##
## select## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layoutplot_ly(x=matrix_product$LD1, y=matrix_product$LD2, z=matrix_product$LD3, type="scatter3d", mode="markers")plot_ly(x=matrix_product$LD1, y=matrix_product$LD2, z=matrix_product$LD3, type="scatter3d", mode="markers", color = train$crime)km <-kmeans(boston_scaled, centers = 6)
plot_ly(x = matrix_product$LD1, y = matrix_product$LD2, z = matrix_product$LD3, type= 'scatter3d', mode='markers', color = km$cluster[ind])